Abelian variety isogeny class 2.243.acc_bul over $\F_{3^{5}}$

• Label: 2.243.acc_bul
• Base field: $\F_{3^{5}}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{3^{5}}$
Dimension:	$2$
L-polynomial:	$1 - 54 x + 1207 x^{2} - 13122 x^{3} + 59049 x^{4}$
Frobenius angles:	$\pm0.0939614996266$, $\pm0.217596874376$
Angle rank:	$2$ (numerical)
Number field:	4.0.2041408.2
Galois group:	$D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$47081$	$3457299073$	$205872547834352$	$12157887004468351929$	$717899340580990565347001$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$190$	$58548$	$14347612$	$3486847940$	$847290206170$	$205891154263974$	$50031545279168062$	$12157665459228029060$	$2954312706539230705252$	$717897987692074601843988$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{3^{5}}$.

Endomorphism algebra over $\F_{3^{5}}$

The endomorphism algebra of this simple isogeny class is 4.0.2041408.2.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.243.cc_bul	$2$	(not in LMFDB)